Why are the camps being closed, forest fire concerns or something like that?
Normally you can send any boy to camp as a provisional. If you're talking about sending your son with your nephew's unit, the easiest way to know if this is okay is to talk to the unit leaders and see if they're willing to take him.
There's no national policy (nor would I imagine national ever making one) to make it more difficult for a boy to attend resident camp of some sort. Even as cub scouts, I've had boys who used to be in my unit but moved across state come back to attend as part of my unit.
The barely 11 thing would probably not be an issue so long as he meets all the joining requirements for boy socuts (10 years old and has earned Arrow of Light). However, LDS units sometimes operate differently. I had two boys who were 10.5 earn AOL and cross from a non-LDS pack to an LDS troop and they had to complete another year of Webelos essentially because of the way their units are set up (strictly by age I believe).
The camp counting between that council and your son's troop…I'm not sure what exactly you mean. Would it count as resident camp towards the 20 nights of camping requirement, or will the activities he'll be participating in count towards the requirements of Tenderfoot, 2nd & 1st Class ranks or merit badges? Should be yes, but I would talk to the SM beforehand to make them aware of the plans and make sure they're on board with everything. They may want to have the SM or ASM (or other designee) that your son is camping with to sign off in his handbook, so they may want them to not sign off in the book so the troop's SM can sign off. There's a proper method for handling that, I can't remember exactly but I'm sure Mr. Cleary could answer better.
Your safest bet is to talk to the leadership of both troops and make sure both are on board and there is a plan in place on how to handle things like advancements, merit badge work, etc.